The nonlinearity in dynamic viscoelastic behavior of brain tissue was investigated. Small samples of white matter of fresh bovine brain tissue were tested using the forced vibration method in simple shear. The brain samples were assumed to be isotropic, homogeneous, and incompressible. It was shown that material nonlinearity was present at Lagrangian shear strain levels as low as 4%. The sample responses were viscoelastic up to 64% shear strain. Two nonlinear viscoelastic models were proposed for the mechanical behavior of brain tissue, namely the fully nonlinear viscoelastic model with multiple hereditary integrals and the quasilinear viscoelastic model with a single hereditary integral. The multiple hereditary integral model was developed to describe the nonlinearity of the material response with respect to strain (spatial nonlinearity) as well as time (temporal nonlinearity). It was shown that the temporal nonlinearity had significant contribution to the nonlinearity of brain tissue. The quasilinear viscoelastic model was shown to be valid only at low frequencies. Using finite element analysis, it was shown that the quasilinear viscoelastic model was not sufficient to describe the nonlinearity observed in brain tissue for variable shear strains more than 4%. The finite element model indicated that stress relaxation test results that are typically used to characterize brain tissue are not accurate for the short time loadings which cause traumatic brain injury.
It was shown experimentally that the first-order material properties of brain tissue were highly dependent on the applied strain level. The magnitude of the linear complex moduli decreased and the phase increased to asymptotic values. The theory of strain conditioning was proposed to describe this phenomenon. It was shown that strain conditioning was the result of unrecoverable changes in the material properties of the samples. The gradual failure of the weaker microstructural bonds between the glial cells and the rest of the brain tissue was proposed as the mechanism of strain conditioning. Strain conditioning was suggested as a necessary condition for describing the mechanical behavior of brain tissue using a nonaging viscoelastic constitutive relation. This theory was successfully applied to unify the sparse available data on the linear viscoelastic properties of brain tissue.
The cumulative outcome of this dissertation is that temporal nonlinearity and strain conditioning are essential considerations in modeling the dynamic viscoelastic behavior of brain tissue.